Why would heater blow warm air while driving but cold air while idling and why would enigine temperature go up while idling and down when driving?

When a vehicle is idling, the engine may not produce enough heat to warm the coolant effectively, leading to cold air from the heater. In contrast, while driving, the engine works harder and generates more heat, allowing the heater to blow warm air. The engine temperature can rise while idling due to reduced airflow through the radiator and less coolant circulation, while driving increases airflow and coolant flow, helping to cool the engine.